On a subclass of uniformly convex functions with fixed second coefficient

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
H. E. Darwish
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Distortion Bounds ◽  
Closure Theorems

AbstractUsing of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

2019 ◽  
Vol 69 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad A. Zaighum ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Extreme Point ◽  
Convex Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Closure Theorems

Abstract Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Generalized Hypergeometric Functions ◽  
Uniformly Convex Functions

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.

scholarly journals On Subclass of -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Waggas Galib Atshan ◽  
Ali Hamza Abada
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Uniformly Convex Functions ◽  
Complex Order

We introduce a subclass of -uniformly convex functions of order with negative coefficients by using the multiplier transformations in the open unit disk . We obtain coefficient estimates, radii of convexity and close-to-convexity, extreme points, and integral means inequalities for the function that belongs to the class .

scholarly journals A New Class of Analytic Functions Associated with Sălăgean Operator

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Arif ◽  
Khurshid Ahmad ◽  
Jin-Lin Liu ◽  
Janusz Sokół
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Coefficient Estimates ◽  
Inclusion Relation ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Distortion Bounds

The main object of the present paper is to investigate a number of useful properties such as inclusion relation, distortion bounds, coefficient estimates, and subordination results for a new subclass of analytic functions which are defined here by means of a linear operator. Several known consequences of the results are also pointed out.

scholarly journals Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
K. Vijaya ◽  
G. Murugusundaramoorthy ◽  
M. Kasthuri
Keyword(s):  
Harmonic Functions ◽  
Extreme Points ◽  
Partial Sums ◽  
Open Unit ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Convolution Properties ◽  
Positive Coefficients ◽  
Complex Valued

Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.

scholarly journals Certain New Classes of Analytic Functions with Varying Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike ◽  
Varying Arguments

We introduce certain new classes κ−VST(α,β) and κ−VUCV(α,β), which represent the κ uniformly starlike functions of order α and type β with varying arguments and the κ uniformly convex functions of order α and type β with varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes.

scholarly journals Subclass of Multivalent Harmonic Functions Defi…ned by Wright Generalized Hypergeometric Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
M. K. Aouf ◽  
A. O. Moustafa ◽  
E. A. Adwan
Keyword(s):  
Harmonic Functions ◽  
Hypergeometric Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Function Coefficient ◽  
Distortion Bounds ◽  
Wright Generalized Hypergeometric Functions

We introduce a new class of multivalent harmonic functions defi…ned by Wright generalized hypergeometric function. Coefficient estimates, extreme points, distortion bounds, and convex combination for functions belonging to this class are obtained.

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